期刊文献+
任意字段
题名或关键词
题名
关键词
文摘
作者
第一作者
机构
刊名
分类号
参考文献
作者简介
基金资助
栏目信息

Weak Continuity of Riemann Integrable Functions in Lebesgue-Bochner Spaces 被引量：1

Weak Continuity of Riemann Integrable Functions in Lebesgue-Bochner Spaces
原文传递
导出
摘要 In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X＊ is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31（2）, 697-703 （2001）] that L^1[0, 1] has the weak Lebesgue property. In general, Banach space-valued Riemann integrable functions defined on [0, 1] （equipped with the Lebesgue measure） need not be weakly continuous almost everywhere. A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere. In this paper we discuss this property for the Banach space LX^1 of all Bochner integrable functions from [0, 1] to the Banach space X. We show that LX^1 has the weak Lebesgue property whenever X has the Radon-Nikodym property and X＊ is separable. This generalizes the result by Chonghu Wang and Kang Wan [Rocky Mountain J. Math., 31（2）, 697-703 （2001）] that L^1[0, 1] has the weak Lebesgue property.
作者 J.M.CALABUIG J.RODRíGUEZ E.A.SNCHEZ-PREZ
机构地区 Instituto Universitario de Matemlica Pura y Aplicada
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2010年第2期241-248,共8页 数学学报（英文版）
基金 supported by MEC and FEDER (Project MTM2005-08350-C03-03) Generalitat Valenciana (Project GV/2007/191) supported by MEC and FEDER (Project MTM2005-08379) Fundacion Seneca (Project 00690/PI/04) the "Juan de la Cierva" Programme (MEC and FSE) supported by MEC and FEDER (Project MTM2006-11690-C02-01)
关键词 Riemann integral Bochner integral Lebesgue-Bochner space weak Lebesgue property Riemann integral, Bochner integral, Lebesgue-Bochner space, weak Lebesgue property
分类号 O177.2 [理学—基础数学] O172.3 [理学—基础数学]
  • 相关文献

参考文献17

  • 1Graves, L. M.: Riemann integration and Taylor's theorem in general analysis. Trans. Amer. Math. Soc., 29(1), 163-177 (1927).
  • 2Gordon, R. A.: Riemann integration in Banach spaces. Rocky Mountain J. Math., 21(3), 923-949 (1991).
  • 3Alexiewicz, A., Orlicz, W.: Remarks on Riemann-integration of vector-wlued functions. Studia Math., 12, 125-132 (1951).
  • 4Kadets, V. M.: On the Riemann integrability of weakly continuous functions. Quaestiones Math., 17(1), 33-35 (1994).
  • 5Wang, C. H., Yang, Z. H.: Some topological properties of Banach spaces and Riemann integration. Rocky Mountain J. Math., 30(1), 393-400 (2000).
  • 6Wang, C. H.: On the weak property of Lebesgue of Banach spaces. Journal of Nanjing University Mathematical Biquartcrly, English Series, 13(2) 150-155 (1996).
  • 7Wang, C. H., Wan, K.: On the weak property of Lebesgue of L^1(Ω, ∑, μ). Rocky Mountain J. Math., 31(2), 697-703 (2001).
  • 8Diestel, J., Uhl Jr., J. J.: Vector measures, American Mathematical Society, Providence, R.I., 1977, With a foreword by B. J. Pettis, Mathematical Surveys, No. 15.
  • 9Fabian, M., Habala, P., Hajek, P., et al.: Functional analysis and infinite-dimensional geometry, CMS Books in Mathematics/Ouvrages de Matheatiques de la SMC, Vol. 8, Springer-Verlag, New York, 2001.
  • 10Diestel, J.: Sequences and series in Banach spaces, Graduate Texts in Mathematics, Voi. 92, Springer-Verlag, New York, 1984.

引证文献1

Acta Mathematica Sinica,English Series
2010年 第2期

相关作者

内容加载中请稍等...

相关机构

内容加载中请稍等...

相关主题

内容加载中请稍等...

浏览历史

内容加载中请稍等...
;
使用帮助 返回顶部